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Re: If J#0, what is the value of J ? [#permalink]
23 Jul 2012, 16:16
1
This post received KUDOS
Expert's post
0^0 is equal to 1 in most mathematical conventions, but not all. Therefore, you can expect that GMAT not to test the subject--it won't show up, and you won't be expected to know it! _________________
QUESTION YOU ARE TALKING ABOUT SHOULD READ: If \(J\neq{0}\), what is the value of \(J\) ?
(1) \(|J| = J^{-1}\) (2) \(J^J = 1\)
Two reasons why should the stem state that \(J\neq{0}\): For statement (1) if \(J=0\) then we'll have \(0^{-1}=\frac{1}{0}=undefined\). Remember you can't raise zero to a negative power. For statement (2) if \(J=0\) then we'll have \(0^0\). 0^0, in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out.
Also notice that saying in the stem that J is an integer is a redundant.
AS FOR THE SOLUTION: If \(J\neq{0}\), what is the value of \(J\) ?
(1) \(|J| = J^{-1}\) --> \(|J|*J=1\) --> \(J=1\) (here J can no way be a negative number, since in this case we would have \(|J|*J=positive*negative=negative\neq{1}\)). Sufficient.
(2) \(J^J = 1\) --> again only one solution: \(J=1\). Sufficient.
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